Theorems · Definition · algebraic topology

SSet.coherentIso.invStructOfEqMapHom

{X : SSet} →
  {x₀ x₁ : X.obj (Opposite.op { len := 0 })} →
    {f : SSet.Edge x₀ x₁} →
      {g : SSet.coherentIso ⟶ X} →
        f.edge = (CategoryTheory.ConcreteCategory.hom (g.app (Opposite.op { len := 1 }))) SSet.coherentIso.hom.edge →
          f.InvStruct

For a simplicial set X, if an edge in X is equal to the image of hom under a morphism of simplicial sets, this edge has an inverse.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.CoherentIso

Cited by

0 results in Mathlib

Foundations

Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound